Activity 8 - Morphological Operations

In this activity, we are to explore the morphological operators erode and dilate. In these operators, the image (A) is affected by a structuring element (B).

Dilation is defined as the set of all z's which are translations of a reflected B that when intersected with A is not the empty set [1]. For different shapes (circle, square, triangle, hollow square, cross), we are to predict the effect of dilation for different structuring elements (square, vertical rectangle, horizontal rectangle, cross). I will present the results and compare them with my predictions as we go along. Below are the results of the operator dilate for different shapes and different structuring elements.

For the dilate operator, I correctly predicted the results for all cases. It was kind of easy, since the dilate operator expands the shape in the direction where the structuring element (SE) is longer, as seen from the effects on the square, triangle, hollow square, and cross. For the circle shape, I expected that the edges of the resulting shape will be flatter (except for the cross SE, which will just expand the circle), which was proven by the results.




For the erode operator, my predictions also matched the results for the square shape for all SE's. It also matched the results for the circle, triangle, hollow square, and cross shapes for the first three SE's. I had difficulty imagining the effect of erosion on the shapes using the cross SE.

In summary, the dilate operator expands the objects in the image along the direction of the SE, or if the SE is symmetric along both axes, it expands the object in all directions. The erode operator reduces the object in the image along the direction of the SE.

The other operators skel and thin were also explored. Below is the original image (left), the image after skel was applied (center) and the image after thin was applied (right).

It seems like the skel operator missed the head, because no lines or other marks appeared in the head area after skeletonization. It, however, correctly followed the curvature of the body parts of the object. It also noticed that as the object reaches its end (from the shoulder to the hand), the result of the skel operator fades out. The results of the thin operator is very different. The head part did not disappear. The arms and legs are stick straight, not following the curvature of the original object. It seems like it only takes the general direction of the part it considers. For example, the arms are generally vertical so in the thinned image, the arms is just a vertical line.

I give myself 9 points for this activity. Majority of my predictions matched the output, and I was able to understand how the operators worked.

Credits are extended to Orly Tarun and Miguel Sison for helpful suggestions.


[1] A8 - Morphological Operations.pdf - Dr. Maricor Soriano